reserve a,b,c,d,e,f for Real,
        k,m for Nat,
        D for non empty set,
        V for non trivial RealLinearSpace,
        u,v,w for Element of V,
        p,q,r for Element of ProjectiveSpace(V);
reserve o,p,q,r,s,t for Point of TOP-REAL 3,
        M for Matrix of 3,F_Real;
reserve pf for FinSequence of D;
reserve PQR for Matrix of 3,F_Real;

theorem Th65:
  for p being FinSequence of REAL st p = |[0,0,0]| holds
  F2M p = <* <* 0 *>, <* 0 *>, <* 0 *> *>
  proof
    let p being FinSequence of REAL;
    assume p = |[0,0,0]|;
    then len p = 3 & p.1 = 0 & p.2 = 0 & p.3 = 0 by FINSEQ_1:45;
    hence thesis by DEF1;
  end;
